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Using a validation set to monitor the convergence of the fugw loss#
In this example, we use 3 fMRI feature maps for training and 2 independant fMRI feature maps for testing to examine the evolutions of a training and a validation loss on 2 low-resolution brain volumes.
import numpy as np
import matplotlib.pyplot as plt
from nilearn import datasets, image, plotting
from scipy.spatial import distance_matrix
from fugw.mappings import FUGW
We first fetch 5 contrasts for each subject from the localizer dataset.
n_subjects = 2
contrasts = [
"sentence reading vs checkerboard",
"sentence listening",
"calculation vs sentences",
"left vs right button press",
"checkerboard",
]
n_training_contrasts = 3
brain_data = datasets.fetch_localizer_contrasts(
contrasts,
n_subjects=n_subjects,
get_anats=True,
get_masks=True,
)
source_imgs_paths = brain_data["cmaps"][0 : len(contrasts)]
target_imgs_paths = brain_data["cmaps"][len(contrasts) : 2 * len(contrasts)]
source_mask = brain_data["masks"][0]
source_im = image.load_img(source_imgs_paths)
target_im = image.load_img(target_imgs_paths)
mask = image.load_img(source_mask)
Downloading data from https://osf.io/download/5d27cdcaa26b340018084b30/ ...
...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d27d80c114a420016058f7d/ ...
...done. (1 seconds, 0 min)
/usr/local/lib/python3.8/site-packages/nilearn/datasets/func.py:893: UserWarning:
`legacy_format` will default to `False` in release 0.11. Dataset fetchers will then return pandas dataframes by default instead of recarrays.
We then downsample the images by 5 to reduce the computational cost.
SCALE_FACTOR = 5
resized_source_affine = source_im.affine.copy() * SCALE_FACTOR
resized_target_affine = target_im.affine.copy() * SCALE_FACTOR
source_im_resized = image.resample_img(source_im, resized_source_affine)
target_im_resized = image.resample_img(target_im, resized_target_affine)
mask_resized = image.resample_img(mask, resized_source_affine)
source_maps = np.nan_to_num(source_im_resized.get_fdata())
target_maps = np.nan_to_num(target_im_resized.get_fdata())
segmentation = mask_resized.get_fdata()
coordinates = np.argwhere(segmentation > 0)
source_features = source_maps[
coordinates[:, 0], coordinates[:, 1], coordinates[:, 2]
].T
target_features = target_maps[
coordinates[:, 0], coordinates[:, 1], coordinates[:, 2]
].T
fig = plt.figure()
ax = fig.add_subplot(projection="3d")
ax.scatter(coordinates[:, 0], coordinates[:, 1], coordinates[:, 2], marker="o")
ax.view_init(10, 135)
# make the panes transparent
ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
# make the grid lines transparent
ax.xaxis._axinfo["grid"]["color"] = (1, 1, 1, 0)
ax.yaxis._axinfo["grid"]["color"] = (1, 1, 1, 0)
ax.zaxis._axinfo["grid"]["color"] = (1, 1, 1, 0)
ax.set_title("3D voxel coordinates")
plt.show()
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:
NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:294: UserWarning:
Resampling binary images with continuous or linear interpolation. This might lead to unexpected results. You might consider using nearest interpolation instead.
We then compute the distance matrix between voxel coordinates.
source_geometry = distance_matrix(coordinates, coordinates)
target_geometry = source_geometry.copy()
In order to avoid numerical errors when fitting the mapping, we normalize both the features and the geometry.
source_features_normalized = source_features / np.linalg.norm(
source_features, axis=1
).reshape(-1, 1)
target_features_normalized = target_features / np.linalg.norm(
target_features, axis=1
).reshape(-1, 1)
source_geometry_normalized = source_geometry / np.max(source_geometry)
target_geometry_normalized = target_geometry / np.max(target_geometry)
We now fit the mapping using the sinkhorn solver and 10 BCD iterations. We use the first 3 feature maps for training and the last 2 for validation. Anatomical kernels are kept identical for both training and validation, as it will usually be the case in practice when aligning real fMRI data.
mapping = FUGW(alpha=0.5, rho=1, eps=1e-4)
_ = mapping.fit(
source_features=source_features_normalized[:n_training_contrasts],
target_features=target_features_normalized[:n_training_contrasts],
source_geometry=source_geometry_normalized,
target_geometry=target_geometry_normalized,
source_features_val=source_features_normalized[n_training_contrasts:],
target_features_val=target_features_normalized[n_training_contrasts:],
solver="sinkhorn",
solver_params={
"nits_bcd": 10,
},
verbose=True,
)
[15:16:40] Validation data for anatomical kernels is not provided. dense.py:202
Using training data instead.
[15:16:49] BCD step 1/10 FUGW loss: 0.024832315742969513 dense.py:512
Validation loss: 0.026611780747771263
[15:17:05] BCD step 2/10 FUGW loss: 0.007541899103671312 dense.py:512
Validation loss: 0.007889322005212307
[15:17:20] BCD step 3/10 FUGW loss: 0.006806281860917807 dense.py:512
Validation loss: 0.0068863932974636555
[15:17:35] BCD step 4/10 FUGW loss: 0.006414642557501793 dense.py:512
Validation loss: 0.006308848038315773
[15:17:51] BCD step 5/10 FUGW loss: 0.0062024896033108234 dense.py:512
Validation loss: 0.005969317629933357
[15:18:06] BCD step 6/10 FUGW loss: 0.0059875245206058025 dense.py:512
Validation loss: 0.005596095230430365
[15:18:21] BCD step 7/10 FUGW loss: 0.005855212919414043 dense.py:512
Validation loss: 0.0053304582834243774
[15:18:37] BCD step 8/10 FUGW loss: 0.00584545498713851 dense.py:512
Validation loss: 0.005313127767294645
[15:18:52] BCD step 9/10 FUGW loss: 0.005844560451805592 dense.py:512
Validation loss: 0.005311604589223862
Plot the evolution of losses on train and test datasets.
fig, ax1 = plt.subplots()
ax1.set_xlabel("BCD Step")
ax1.set_ylabel("FUGW loss", color="black")
ax1.tick_params(axis="y", labelcolor="black")
ax1.plot(mapping.loss_steps, mapping.loss["total"], color="blue")
ax1.plot(mapping.loss_steps, mapping.loss_val["total"], color="red")
plt.title("Training and validation losses")
plt.legend(["Train", "Validation"])
fig.tight_layout() # otherwise the right y-label is slightly clipped
plt.show()
Plot the alignment of the second validation feature map and project it on the fsaverage5 surface.
example_array = np.nan_to_num(source_im_resized.slicer[..., -1].get_fdata())
example_array /= np.max(np.abs(example_array))
example = image.new_img_like(source_im_resized, example_array)
plotting.view_img_on_surf(example, threshold="50%", surf_mesh="fsaverage5")
Total running time of the script: ( 2 minutes 18.484 seconds)
Estimated memory usage: 8 MB